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Chapter 2: Q 5. (page 237)

Find the derivatives off(x)=x.

Short Answer

Expert verified

The derivative off(x)=xis12x.

Step by step solution

01

Given Information 

The given expression isf(x)=x.

02

Simplification  

f'(x)=limx鈫�0f(x+h)-f(x)hf'(x)=limh鈫�0x+h-xh=limh鈫�0(x+h-x)脳(x+h+x)h.(x+h+x)=limh鈫�0x+h-xh(x+h+x)=limh鈫�01x+h+x=12x

Therefore, the derivate off(x)=xis12x.

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Most popular questions from this chapter

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that is perpendicular to the tangent line to f(x)=x4+1at x=2 and also passes through the point(-1,8)

In Exercises 69鈥�80, determine whether or not f is continuous and/or differentiable at the given value of x. If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.

fx=x2-3,ifx<3x+2,ifx鈮�3,x=3

Sketch a graph of the associated slope function f' for each function f.

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=x2+1

Each graph in Exercises 31鈥�34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

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